Best Known (76, 76+8, s)-Nets in Base 2
(76, 76+8, 524288)-Net over F2 — Constructive and digital
Digital (76, 84, 524288)-net over F2, using
- net defined by OOA [i] based on linear OOA(284, 524288, F2, 8, 8) (dual of [(524288, 8), 4194220, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(284, 2097152, F2, 8) (dual of [2097152, 2097068, 9]-code), using
- 1 times truncation [i] based on linear OA(285, 2097153, F2, 9) (dual of [2097153, 2097068, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(285, 2097153, F2, 9) (dual of [2097153, 2097068, 10]-code), using
- OA 4-folding and stacking [i] based on linear OA(284, 2097152, F2, 8) (dual of [2097152, 2097068, 9]-code), using
(76, 76+8, 699050)-Net over F2 — Digital
Digital (76, 84, 699050)-net over F2, using
- net defined by OOA [i] based on linear OOA(284, 699050, F2, 8, 8) (dual of [(699050, 8), 5592316, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(284, 699050, F2, 7, 8) (dual of [(699050, 7), 4893266, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(284, 699050, F2, 3, 8) (dual of [(699050, 3), 2097066, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(284, 2097150, F2, 8) (dual of [2097150, 2097066, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(284, 2097152, F2, 8) (dual of [2097152, 2097068, 9]-code), using
- 1 times truncation [i] based on linear OA(285, 2097153, F2, 9) (dual of [2097153, 2097068, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(285, 2097153, F2, 9) (dual of [2097153, 2097068, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(284, 2097152, F2, 8) (dual of [2097152, 2097068, 9]-code), using
- OOA 3-folding [i] based on linear OA(284, 2097150, F2, 8) (dual of [2097150, 2097066, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(284, 699050, F2, 3, 8) (dual of [(699050, 3), 2097066, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(284, 699050, F2, 7, 8) (dual of [(699050, 7), 4893266, 9]-NRT-code), using
(76, 76+8, 4641754)-Net in Base 2 — Upper bound on s
There is no (76, 84, 4641755)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 19 342814 738523 307963 660446 > 284 [i]